For f(x), the transformation of the function is stated in the first column. Determine the type of transformation

The solutions to the quadratic problem are x = -1 and x= 4

From the question, we are to create a problem with a quadratic equation and solve graphically

Consider the quadratic equation

x² -3x -4 = 0

The graph of the quadratic equation is shown below

We can observe that the graph cuts the x-axis at the point x = -1 and x = 4

Hence, the solutions to the quadratic problem are x = -1 and x= 4

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x = child tickets

y = adult tickets

x + y = 141

5.60x + 9.30y = 974.60

y = 141 - x

5.60x + 9.30 ( 141 - x ) = 974.60

5.60x + 1311.3 - 9.30x = 974.60

-3.70x + 1311.3 = 974.60

-3.70x = 974.60 - 1311.3

-3.70x = -336.7

x = 91

91 child tickets were sold that day

In the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.

A quadratic equation is a polynomial of degree 2, in a single variable x.

The standard form of a quadratic equation is ax² + bx + c = 0.

The quadratic formula is used to find the solution(s)/root(s) of this equation.

The quadratic formula is:

[tex]x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Thus, identifying the values of a, b, and c, is the first step in using the quadratic formula to find a solution(s)/root(s) to a quadratic equation.

In the question, we are asked to find the values of a, b, and c, in the given quadratic equation - 3x² - 5x + 9 = 0.

To find the values of a, b, and c, we compare the given equation, to the standard form of a quadratic equation, ax² + bx + c = 0.

On comparing, we get a is the coefficient of x², that is, a = -3.

On comparing, we get b is the coefficient of x, that is, b = -5.

On comparing, we get c is the constant term, that is, c = 9.

Thus, in the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.

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The provided question is incomplete.

The complete question is:

"Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.

What are the values a, b, and c in the following quadratic equation?

- 3x² - 5x + 9 = 0

Answer:

2.603 degrees

Step-by-step explanation:

This word problem is talking about a triangle. 500 meters high would be the height and 11 Kilometers would be the base. We should convert kilometers to meters in order to make this easier. 11 kilometers = 11,000 meters.

Height = 500

Base = 11,000

The hypotenuse ends up being 11,011.35777

in order to find the angle of depression (assuming it is a constant rate) we would measure the angle where the hypotenuse meets the base. (11,000 & 11,011.35777) the angle comes out at 2.603 degrees. Hope this helped!

The common difference based on the sequence given is 15.

It should be noted that the sequence given Isa arithmetic sequence.

The common difference will be the second term minus the first term. This will be:

= 101 - 86

= 15

In conclusion, the difference is 15.

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Answer: 2890

Step-by-step explanation:

a = b x p%

= 1700 x 170%

= 1700 x 1.7

= 2890

the population would be 2890 fish after one year

A single card is drawn from each of two decks of 52 cards. The probability of getting a heart from the first deck and then a diamond on the second deck is 6.25%.

Probability means possibility.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

There are 52 cards in a standard deck.

So, the total number of possible outcomes=52

We have to pick a single card from each of decks of 52 cards.

In a deck of 52 cards there are 13 heart cards and 13 diamond cards.

Therefore the probability of getting a heart from the first deck=13/52

And the probability of getting a diamond from the second deck=13/52

Hence the probability of getting a heart from the first deck and then a diamond on the second deck=(13/52)×(13/52)=6.25%

Thus, the probability of getting a heart from the first deck and then a diamond on the second deck is 6.25%.

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Answer:

6.25%

Step-by-step explanation:

I got it right on the test.

Answer:

[tex]3 \sqrt{2} [/tex]

Step-by-step explanation:

You can the distance between P(10,-7) and Q(7,-10) by using 'PQ=

[tex] \sqrt{(10 - 7) ^{2} } + \sqrt{ ( - 7 + 10) ^{2} } [/tex]

Also, for example the distance between A(a,b) and B(c,d)

is

[tex] \sqrt{(a - c)^{2} } + \sqrt{(b - d) ^{2} } [/tex]

Answer:

[tex]\sqrt{18}[/tex] or [tex]3\sqrt{2}[/tex] units.

Step-by-step explanation:

To find the distance between two points, we can use the Distance Formula.

Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given:

P (10, -7) ⇒ x₁ = 10, y₁ = -7

Q (7, -10) ⇒ x₂ = 7, y₂ = -10

Substitute the given values into the formula and simplify.

[tex]\\\implies d=\sqrt{\bold{(7-10)}^2+\bold{(-10-(-7))}^2}\\\\\implies d=\sqrt{\bold{(-3)}^2+\bold{(-10+7)}^2}\\\\\implies d=\sqrt{9+\bold{(-3)}^2}\\\\\implies d=\sqrt{\bold{9+9}}\\\\\implies d=\sqrt{\bold{18}}\\\\\implies d=\sqrt{\bold{9}\times2}\\\\\implies d=3\sqrt{2}[/tex]

The distance between points P and Q is [tex]\sqrt{18}[/tex] or [tex]3\sqrt{2}[/tex] units.

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Answer:

on a coordinates plane :

The point of coordinates (h , k) is the center of the circle.

Step-by-step explanation:

by definition the expression:

(x-h)² + (y-k)² = r²

is the equation of the circle (in standard form)

Where r is the radius and (h , k) is the center of the circle.

It is the general equation of a circle

Correct answer:

The general equation of a circle is [tex](x - h)^2 + (y - k)^2 = r^2,[/tex]where (h, k) represents the location of the circle's center, and r represents the length of its radius. if we take some entities as [tex]h=4,k=-3[/tex] first has the equation of [tex](x - 4)^2 + (y + 3)^2 = 29[/tex]. This means that its center must be located at (4, –3), and its radius is √29.

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The complete factorisation of the polynomial given; x³ + 2x² + 4x + 8 as in the task content can be factorised and determined as; Choice D; (x+2)(x+2i)(x-2i).

It follows from the given task content that the polynomial whose factors are to be determined by means of factorisation is; x³ + 2x² + 4x+8.

It follows from observation that one of the zeros of the polynomial expression is at; x = -2.

Consequently, one of the factors of the polynomial in discuss is; (x+2).

x³ + 2x² + 4x+8 = (x+2) (x² - 4i²)

= (x+2)(x+2i)(x-2i)

Consequently, it follows that the complete factorisation of the polynomial is; (x+2)(x+2i)(x-2i).

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Answer:

y = 3/2x -15

Step-by-step explanation:

y = mx + b this is the slope intercept form.  We need the slope and the y intercept.  The slope (m) has been given (3/2), we just need the b (y-intercept).  We will use the point given to find b.  The point given is (8,-3).  8 is the x term and -3 is the y term.  We will plug them into y = 3/2x + b to solve for b.

y = mx + b

y = (3/2) x + b   The slope was given

-3 = (3/2)(8) + b  Plugged in the given x and y from the point (8, -3)

-3 = 12 + b  I can make 8 into a fraction by putting a 1 under it.

                   (3/2)(8/1).  I can cross cancel to make the number easier to

                    2 and 8 both share the factor 2 so I will divide both numbers

                   by 2 and I will now have (3/1)(4/1).  3x4 is 12 and 1x1 is 1, so

                   12/1 is  the same as 12.

-15 = b      Subtract both sides by 12.  -3-12 is -15

Now that I have the m and the b, I can write the equation in the slope intercept form.  y =  3/2 + (-15) or y = 3/2 -15    

Answer:

The number 23 is prime. Therefore, the cube root of 23 = ∛23 = 2.8439.

Step-by-step explanation:

Answer:

-2 and -3

Step-by-step explanation:

The minimum of |sin 3x| is 0 and the max is 1 (since the sine function ranges from -1 to 1)

Therefore, the maximum is 1 - 3 = -2 and the minimum is 0 - 3 = -3.

He pays $0.24 less when using his loyalty card.

We know that, without the card, he would pay $1.679 dollars per liter of gasoline.

With his card, he would pay $1.439

To find the relation between the two prices, we just need to take the difference between the two values (a difference is a subtraction).

d = $1.679 - $1.439 = $0.24

He pays $0.24 less when using his loyalty card.

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The type of motion which transforms the letter “p” into a “b” is; Reflection.

It follows that the task content demands that the type of motion which maps p to b be identified. On this note, it follows that the type of motion in discuss is Reflection. More particularly, a reflection over the horizontal axis most definitely causes this transformation.

Therefore, the motion which transforms the letter “p” into a “b” is; Reflection.

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Answer:

The answer to your question is m = 6

Step-by-step explanation:

I hope this helps and have a good day!

Answer:

36^12 - m = 6^2m

6^2(12 - m) = 6^2m

24 - 2m = 2m

24 = 4m

m = 6

Answer:

108°

Step-by-step explanation:

We know for a theorem that A = B, so:

4x + 28 = 2x + 68

Isolating the x:

2x = 40

x = 20

Now let's plug in the equation for A:

4(20) + 28 = 108°

Answer: draw the line using a ruler on which you have identified points 2 7/16 inches apart

Step-by-step explanation:  On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches

Answer:

Step-by-step explanation:

In the quadratic form ...

  (x -h)² = 4p(y -k)

The value 4p is the length of the latus rectum. It also tells the distance between the vertex (h, k) and the focus (h, k+p).

The value of 4p is given as 8. This means p = 8/4 = 2.

The length of the latus rectum is 8.

The end points of the latus rectum have the same y-value as the focus:

  y = k +p = -1 +2 = 1

The end points of the latus rectum have x-values that are h±2p.

  x = h ± 2p = -4 ± 2·2 = {-8, 0}

The end points of the latus rectum are (-8, 1) and (0, 1).

The function which compares the growth of both functions is; The function y = 3x is growing slower than y = 3^x.

The graphs in the task content are given as y=3x which is a linear graph, and y=3^x which is the exponential graph.

Hence, it follows that although both graphs are growing, the graph of function y = 3x is growing slower than y = 3^x.

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Answer:  30 miles

Work Shown:

2 in : 6 mi

5*2 in : 5*6 mi

10 in : 30 mi

It would cost $72,000 for 7 units of that product.

The term “discount” refers to the pricing system in which the price of a commodity (goods or services) is lower than its marked price listed price. It is simply to say, 'discount' is a percentage of the listed price. A discount is a kind of price deduction in products that is noticed in consumer transactions, where the buyers have proposed a percentage of rebates on various products in order to boost sales. This rebate offered by the seller to buyer is known as a discount.

Original cost of product = $15,000.

For the second product there is a discount of 15%, thus selling price for the second product = $15,000 x 0.85 = $12750

For the fourth product and on there is a discount of 30%, thus selling price for the fourth product and on = $15,000 x 0.70 = $10500.

Thus total price of 7 units =  $15,000 + $12750x2 + $10500x3

=   $15,000 +   $25,500 + $31500

= $72,000

Thus it would cost $72,000 for 7 units of that product.

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See below for the response to each question

This is the item that is being surveyed.

The surveyed item is birth weights

Hence, the variable is birth weights

From the question, we have:

Average birth weight is 6 pounds 8 ounces.

Hence, the units of the variable are pounds and ounces

This is the total number of babies in Southeast Asia

Hence, the population of interest is the babies in Southeast Asia

This is the people in the survey

Hence, the individual in the study is the 100 babies that were randomly surveyed

This is the value that gives the required information.

Hence, the parameter of interest is the average birth weight

The statistic is the average

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The expected value for the person buying the insurance is -25.

The expected value is the average gain or loss of an event if the event is repeated a number of times.

Expected value = ∑xP(x)

It is given that,

The probability of a 47-year-old woman passing away during the coming year is 0.179% = 0.00179

The death benefit = $100,000 - $204 = $99,796

The loss from living = -204

Then the expected value = 99796(0.00179) + (-204)(0.99821) = -25

Therefore, the expected value for the person buying the insurance is -25.

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The bearing angle exists 53.49°.

A bearing of 36° corresponds to the corresponding angle of

θ = 90 -36 = 54°

The (x, y) values for the position of the ship after achieving its first heading exist:

[tex]x_1[/tex] = 12.1 Cos 54° = 7.11 m

[tex]y_1[/tex] = 12.1 Sin 54° = 9.78 m

Our second displacement exists a simple 4.6 mi due east, that exists, the positive x-direction. The components exist therefore

[tex]x_2[/tex] = 6.1 mi

[tex]y_2[/tex] = 0 mi

To find the total displacement from the port, we'll add these two vectors' components and use the distance formula:

Δx [tex]= x_1+x_2[/tex]

= 7.11 mi + 6.1 mi = 13.21 mi

Δy [tex]=y_1+y_2[/tex]

= 9.78 mi + 0 mi = 9.78 mi

[tex]$r=\sqrt{(x_{total})^2+(y_{total})^2}[/tex]

[tex]=\sqrt{(13.21mi)^2+(9.78mi)^2}[/tex]

= 16.43 mi

The direction of the displacement vector exists given by

tan θ = Δy/Δx

θ = arc tan (Δy/Δx)

= arc tan (9.78/13.21)

= 36.51°

The question requested for the bearing angle, which exists just this angle subtracted from 90°:

90° - 36.51° = 53.49°.

Therefore, the bearing angle exists 53.49°.

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Answer:

Step-by-step explanation:

The value of tan theta from the given. expression is  7/√51

Trigonometry identity are expressions written in terms of sine, cosine and tangents.

Given the following trigonometry values as shown:

sin(theta)=0.7

Convert the decimal to fractions

sin(theta)= 7/10

According to SOH CAH TOA;

sin theta = opp/hyp

Determine the adjacent

adj = √hyp²-opp²

Substitute the values;

adj = √10²-7²

adj = √100-49

adj = √51

Determine the value of tan theta

tan(theta) = opp/adj

Substitute

tan(theta) = 7/√51

Hence the value of tan theta from the given. expression is  7/√51

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The area of the triangle is 1000 unit square

The area of a triangle is half the base multiplied by the height

The formula is given as;

Area = 1/2 × b × h

From the information given, the base is given as 50 and the height is 40

Area = 1/ 2 × 50 × 40

Area = 1/ 2 × 2000

Area = 1000 unit square

Thus, the area of the triangle is 1000 unit square

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